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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

A Transformation Approach to Optimal Control Problems with Bounded State Variables

A technique is described and utilized in the study of the solutions to various general problems in optimal control theory, which are converted in to Lagrange problems in the calculus of variations. This is accomplished by mapping certain properties in Euclidean space onto closed control and state regions. Nonlinear control problems with a unit m cube as control region and unit n cube as state region are considered.

Hanafy, Lawrence Hanafy↗
NASA NTRS1972

Application of quadratic optimization to supersonic inlet control.

This paper describes the application of linear stochastic optimal control theory to the design of the control system for the air intake, the inlet, of a supersonic air-breathing propulsion system. The controls must maintain a stable inlet shock position in the presence of random airflow disturbances and prevent inlet unstart. Two different linear time invariant controllers are developed. One is designed to minimize a nonquadratic index, the expected frequency of inlet unstart, and the other is designed to minimize the mean square value of inlet shock motion. The quadratic equivalence principle is used to obtain a linear controller that minimizes the nonquadratic index. The two controllers are compared on the basis of unstart prevention, control effort requirements, and frequency response. It is concluded that while controls designed to minimize unstarts are desirable in that the index minimized is physically meaningful, computation time required is longer than for the minimum mean square shock position approach. The simpler minimum mean square shock position solution produced expected unstart frequency values which were not significantly larger than those of the nonquadratic solution.

Lehtinen, B.↗
NASA NTRS1973

Limiting performance of dynamic systems subject to random inputs

The problem of determining the limiting performance characteristics of mechanical systems subject to random input is studied. A review is presented of the classical work in the optimal design of stochastic systems. Some recent results of stochastic optimal control theory are employed. The solution to the limiting performance problem is formulated in both the frequency and time domains. Both formulations require substantial, burdensome computations when applied to large scale systems.

Pilkey, W. D.↗
NASA NTRS1974

Transient response of multidegree-of-freedom linear systems to forcing functions with inequality constraints

Optimal control theory is applied to analyze the transient response of discrete linear systems to forcing functions with unknown time dependence but having known bounds. Particular attention is given to forcing functions which include: (1) maximum displacement of any given mass element, (2) maximum relative displacement of any two adjacent masses, and (3) maximum acceleration of a given mass. Linear mechanical systems with an arbitrary number of degrees of freedom and only one forcing function acting are considered. In the general case, the desired forcing function is found to be a function that switches from the upper-to-lower bound and vice-versa at certain moments of time. A general procedure for finding such switching times is set forth.

Michalopoulos, C. D.↗
NASA NTRS1973

The preview control problem with application to man-machine system analysis

The preview control problem is formulated in a general form and its solution is obtained. The analytical tool used is discrete stochastic optimal control theory. Aiming the application to manual control situations with preview, time delay, observation noise, motor noise, etc. were included in formulating the problem. Manual preview control experiments were performed to qualitatively check the validity of the model, and it was found that the mechanism of the manual control problem was explained by the developed model.

Tomizuka, M.↗
NASA NTRS1975

Terminal guidance and navigation for comet and asteroid rendezvous

A terminal guidance and navigation scheme developed in earlier work was modified and evaluated for a solar electric propulsion rendezvous mission to comet Encke. The scheme is intended for autonomous, on-board use. The guidance algorithm is based on optimal control theory and minimizes the time integrated square of thrust acceleration. The navigation algorithm employs a modified Kalman filter set in measurement variables. Random sequences were generated to simulate measurement errors, and the evaluation was conducted with detailed numerical computations which include actual motions of spacecraft and comet. The evaluations showed that the scheme attains rendezvous and maintains station after rendezvous within less than 10 km for estimated best measurements and within less than 100 km for estimated worst measurements. The measurements required are angles, range, and range rate. Angles and range appear to be absolutely necessary; range rate is not as strong a measurement type, and further modifications of the filter will allow a scheme that does not require the rate measurements.

Bennett, A. G.↗
NASA NTRS1976

A method for developing K/S boundary conditions

A method for developing the missing general K/S (Kustaanheimo/Stiefel) boundary conditions is presented, with use of the formalism of optimal control theory. As illustrative examples, the method is applied to the transfer between two position and velocity vectors and to the K/S Lambert problem to derive the missing terminal conditions. The necessary equations for a solution are then developed to the K/S Lambert problem with both the fictitious time, s, and the generalized eccentric anomaly, E, as the independent variables. The latter formulation, requiring the solution of only one nonlinear, well-behaved equation in one unknown, E, results in considerable simplification of the problem. This simplification is possible because the energy equation, in the E-formulation, is separable.

Jezewski, D. J.↗
NASA NTRS1976

Stability and control of maneuvering high-performance aircraft

Stability and control characteristics of a high-performance aircraft have been examined over a wide range of maneuvering flight conditions, in order to identify general rules for the design of departure-preventing control systems. This has been accomplished using fully coupled linear dynamic models which account for nonzero mean values of aerodynamic angles and angular rates. Stability augmentation systems derived from optimal control theory are shown to maintain stable, well-damped aircraft dynamics over a wide range of maneuvering flight conditions. This design approach generates cross-feeds and control interconnects (as well as conventional feedback terms) for improved aircraft stability.

Stengel, R. F.↗
NASA NTRS1976

High angle-of-attack stability-and-control analysis

Methods of linear systems analysis were applied to mathematical models of aircraft flying at high angle of attack and maneuver rate. First order longitudinal and lateral directional coupling is obtained by linearizing the complete nonlinear equations of motion about a generalized (quasi steady) trim point. Open loop stability boundaries are defined using the linear dynamic equations, and pilot in the loop effects are presented. Stability augmentation structures for maneuvering flight conditions are shown to be defined readily using optimal control theory.

Stengel, R. F.↗
NASA NTRS1975

Guidance of an aeromaneuvering orbit-to-orbit shuttle through a statistically varying atmosphere

One candidate for a reusable upper stage to be carried by the space shuttle is an aeromaneuvering orbit-to-orbit shuttle (AMOOS). This concept uses the drag of the vehicle during a pass through the atmosphere rather than the propulsion system to slow the vehicle on a return from a high energy orbit. The nature and magnitude of the sensitivity of AMOOS to uncertainties in the properties of the atmosphere are shown. Various guidance schemes for correcting for the effects that the unpredictable variations in the atmosphere have on the trajectory are discussed. For the mission studied here, a payload retrieval from geosynchronous orbit with aerodynamic plane change, a linear feedback guidance scheme was developed. A relatively simple heuristic law was used to demonstrate the concept. Using optimal control theory a feedback law was developed analytically. Testing with a large number of different atmospheres showed this law to be a feasible means of controlling the AMOOS trajectory. Refinements to the technique offer promise of significant improvement, and these are discussed.

Rehder, J. J.↗
NASA NTRS1976

K/S two-point-boundary-value problems

A method for developing the missing general K/S (Kustaanheimo/Stiefel) boundary conditions is presented, with use of the formalism of optimal control theory. As an illustrative example, the method is applied to the K/S Lambert problem to derive the missing terminal condition. The necessary equations are developed for a solution to this problem with the generalized eccentric anomaly, E, as the independent variable. This formulation, requiring the solution of only one nonlinear, well-behaved equation in one unknown, E, results in considerable simplification of the problem.

Jezewski, D. J.↗
NASA NTRS1977

Optimal controls for an advanced turbofan engine

Linear optimal control theory is applied to the control synthesis of a high bypass ratio, variable pitch, turbofan engine. The basic control philosophy is to use only a low order dynamic model of the plant coupled with the concept of integral-output states so as to maintain control simplicity yet guarantee integral control of thrust, turbine temperature and other important engine outputs. Linear simulation results indicate that the control system developed provides rapid control of small thrust perturbations and quickly eliminates the effect of unmodelled thrust and temperature disturbances. Large thrust accelerations are obtained in about one half second while the control maintains negligible overshoot in temperature and stall margins.

Slater, G. L.↗
NASA NTRS1978

Analytical design of a high performance stability and control augmentation system for a hingeless rotor helicopter

A stability and control augmentation system (SCAS) was designed based on a set of comprehensive performance criteria. Linear optimal control theory was applied to determine appropriate feedback gains for the stability augmentation system (SAS). The helicopter was represented by six-degree-of-freedom rigid body equations of motion and constant factors were used as weightings for state and control variables. The ratio of these factors was employed as a parameter for SAS analysis and values of the feedback gains were selected on this basis to satisfy three of the performance criteria for full and partial state feedback systems. A least squares design method was then applied to determine control augmentation system (CAS) cross feed gains to satisfy the remaining seven performance criteria. The SCAS gains were then evaluated by nine degree-of-freedom equations which include flapping motion and conclusions drawn concerning the necessity of including the pitch/regressing and roll/regressing modes in SCAS analyses.

Miyajima, K.↗
NASA NTRS1979

Application of two synthesis methods for active flutter suppression on an aeroelastic wind tunnel model

Two flutter suppression control laws have been synthesized, implemented, and demonstrated on an aeroelastic wind-tunnel model of a transport-type wing. One control law was synthesized using an aerodynamic energy method and the other from using results of optimal control theory. At M = 0.95, the model was tested to a dynamic pressure 44 percent above the system-off flutter dynamic pressure. Both synthesis methods yielded control laws effective in suppressing flutter. The experimental results also indicate that wind-tunnel turbulence is an important factor in the experimental demonstration of system performance.

Abel, I.↗
NASA NTRS1980

Application of two design methods for active flutter suppression and wind-tunnel test results

The synthesis, implementation, and wind tunnel test of two flutter suppression control laws for an aeroelastic model equipped with a trailing edge control surface are presented. One control law is based on the aerodynamic energy method, and the other is based on results of optimal control theory. Analytical methods used to design the control laws and evaluate their performance are described. At Mach 0.6, 0.8, and 0.9, increases in flutter dynamic pressure were obtained but the full 44 percent increase was not achieved. However at Mach 0.95, the 44 percent increase was achieved with both control laws. Experimental results indicate that the performance of the systems is not so effective as that predicted by analysis, and that wind tunnel turbulence plays an important role in both control law synthesis and demonstration of system performance.

Newsom, J. R.↗
NASA NTRS1980

The dynamics and control of large flexible space structures, 3. Part A: Shape and orientation control of a platform in orbit using point actuators

The dynamics, attitude, and shape control of a large thin flexible square platform in orbit are studied. Attitude and shape control are assumed to result from actuators placed perpendicular to the main surface and one edge and their effect on the rigid body and elastic modes is modelled to first order. The equations of motion are linearized about three different nominal orientations: (1) the platform following the local vertical with its major surface perpendicular to the orbital plane; (2) the platform following the local horizontal with its major surface normal to the local vertical; and (3) the platform following the local vertical with its major surface perpendicular to the orbit normal. The stability of the uncontrolled system is investigated analytically. Once controllability is established for a set of actuator locations, control law development is based on decoupling, pole placement, and linear optimal control theory. Frequencies and elastic modal shape functions are obtained using a finite element computer algorithm, two different approximate analytical methods, and the results of the three methods compared.

Bainum, P. M.↗
NASA NTRS1980

Optimal large angle maneuvers with simultaneous shape control/vibration arrest

A relaxation method is demonstrated which reliably solves the nonlinear two point boundary value problem which arises when optimal control theory is applied to determination of large angle maneuvers of flexible spacecraft. The basic ideas are summarized and several idealized maneuvers are determined. The emphasis is upon demonstrating the basic ideas and practical aspects of the methodology.

Turner, J. D.↗